What's the point of such a flight? Just from looking at the map, it looks like there might be 100 people on Papa Westray, maybe 1000 on Westray, with several ferry routes. The only rationale I can think of is maybe if the guy who owns most of Papa Westray lives on Westray, flies back and forth on a regular basis, and keeps the plane running for his tennants and neighbors.

It's so the airline doesn't have to do a separate flight to each island. AFAIK the main purpose is to go to and from Kirkwall (and from there on to wherever), not between the islands.